Friction and inertia of a vortex in an underdamped Josephson array

We study the motion of massive vortices in Josephson-junction arrays by numerically solving the equations of motion for square lattices of resistively and capacitively shunted Josephson junctions. We find that the viscous drag force on a vortex, which varies as the inverse of the junction resistance for low-mass vortices, becomes independent of the junction resistance as the vortex mass increases. We present a semiquantitative model that explains this unusual behavior. As a consequence of the excess drag, ballistic vortex motion should only be observed for a limited range of parameter values, in agreement with the recent experiment of Van der Zant et al. [Europhys. Lett. 18, 343 (1992)].